According to show writer Marc Cherry in Golden Girls Forever, the show nearly got sued over this episode. There'd been a joke where Mother Superior asks Sophia why she found a copy of Dianetics in her room. Sophia says "Dianetics?, I thought it said 'Diuretics!'" The Church of Scientology threatened to sue, but Paul Junger Witt and Tony Thomas decided to remove the reference instead of fighting it in court.
The title of this episode comes from the movie musical The Sound of Music (1965) in which the mother superior sings Maria which includes the lyric "How do you solve a problem like Maria?".
Kathleen Freeman who plays the Reverend Mother in Sophia's convent also memorably played the nun who raised Jake and Elwood in The Blues Brothers (1980).
Blanche's opposition to being a nun is doubly funny when one realizes that Rue McClanahan would assume the role of Mother Superior in 1993's "Nunsense" and several of its sequels.